In recent years numerous adhesives using polyamides, polyesters, polyacrylates, etc. as their effective components have been developed in rapid succession. Particularly, various polyester adhesives improved in adhesive strength, mechanical properties and thermal properties are being studied from numerous angles. While the present inventors have carried out one research after another on various types of polyester adhesives, there has been felt a need for developing polyester adhesives possessed of further advanced adhesive properties to meet increasingly wider diversifications in methods of adhesion, varieties of substrates subjected to adhesion, attributes expected of adhesives such as, for example, various forms of adhesive strength including shear strength and peel strength and to satisfy requirements for higher levels of thermal, mechanical and electrical properties. The conventional polyester adhesives such as those of polyethylene terephthalate-sebacate, polyethylene-tetramethylene terephthalate-adipate, polytetramethylene terephthalate-isophthalate, and polytetramethylene terephthalate-isophthalate-sebacate exhibit relatively low adhesive strength to metals compared with other forms of adhesive strength. They have, consequently, entailed a disadvantage that their effective use is obtained on limited kinds of substrates and they fail to provide necessary adhesion to building materials, mechanical parts, electrical devices and so on which demand high adhesive strength.